I hope that someone could give me some hints or tips on how to approach this question, even though these types of questions are usually closed off as homework.

A burner is run by a fuel mixture of $\pu{90 mol.\%}$ ethanol and $\pu{10 mol.\%}$ water. Assume a complete combustion with air ($\pu{79 mol.\%}$$\ce{N2}$, $\pu{21 mol.\%}$$\ce{O2}$). The whole process takes place at $\pu{100 kPa}$.

Calculate the inlet flow rate of the fuel given that the flow rate of air is $\pu{100 mol s-1}$ and that the excess of air is $20\%$.

The answer key only gives the answer $\pu{6.48 mol s-1}$ of the fuel without explaining the calculations.

My attempt at the question was:

$$\ce{C2H5OH + H2O + 3O2 -> 2CO2 + 4H2O}$$

Knowing that we have $20\%$ excess in air, we could calculate the theoretical moles needed.

$\begingroup$A burner combusts fuel. What takes part in such reactions?$\endgroup$
– Eashaan GodboleJan 11 at 14:54

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$\begingroup$Also, the question looks like just stoichiometry. Why did you include a heat exchanger etc?$\endgroup$
– Eashaan GodboleJan 11 at 15:01

$\begingroup$@EashaanGodbole I added the water in the reaction since they stated in the problem that the fuel consisted of both ethanol and water, although I know that a combustion reaction does not include water in the reactants. The diagram of the system was given, there are other questions which involve the heat exchanger specifically.$\endgroup$
– JohanJan 11 at 15:16

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$\begingroup$The inlet water should not be included in the balanced chemical reaction formula, and you balanced the formula incorrectly. Your first step should be to get that right.$\endgroup$
– Chester MillerJan 11 at 17:12

2 Answers
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I think you overcomplicate the problem. There are many variables you don't need and many components that are duds (nitrogen, water, pressure). What important is that we burn ethanol:

$$\ce{C2H5OH + 3 O2 -> 2 CO2 + 3 H2O}$$

so that the ratio between ethanol and oxygen is $1:3$. I have taken chemistry engineering classes long time ago and I don't remember exact notations, so I'd rather denote molar flow rate with an n-dot notation:

You calculated 83.3 moles of air reacting with the ethanol. Since air is 21% oxygen, this means that 83.3 x 0.21 = 17.5 moles of oxygen react with the ethanol. Since each mole of ethanol reacts with 3 moles of oxygen, the number of moles of ethanol that react is 17.5/3=5.833 moles ethanol. Since the fuel mixture is 90% ethanol, there are 10 moles of fuel mixture for every 9 moles of ethanol. So the number of moles of fuel mixture are 5.833 x 10/9=6.48 moles of fuel mixture.